Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
420 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #23763416 | C2 | semidirect |
| 3. #23762170 | C2 | semidirect |
| 5. #23761723 | C2 | semidirect |
| 6. #23761259 | C2 | semidirect |
| 189. C79 | #10467 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772868 | 2 |
| #23763416 | 2 |
| #23762170 | 2 |
| #23761960 | 2 |
| #23761723 | 2 |
| #23761259 | 2 |
| C79×#1540 | 2 |
| #10467 | 79 |